测量误差对单位根检验的影响  

Influence of Measurement Error in Unit Root Test

作　　者：刘田[1] 谈进[2] 史代敏[1] 

机构地区：[1]西南财经大学统计学院,四川成都610074 [2]西南财经大学经济信息工程学院,四川成都610074

出　　处：《数理统计与管理》2014年第6期991-1000,共10页Journal of Applied Statistics and Management

基　　金：国家自然科学基金项目(71171166);中央高校基本科研业务费项目(JBK120405)资助

摘　　要：本文推导了加性平稳测量误差下单位根检验中有截距和无截距情形下T(p-1)与τ两种统计量的极限分布。理论分析和蒙特卡罗实验均表明,单位根检验结果易受到测量误差的影响。测量误差将导致统计量分布向左偏移,从而导致检验水平的扭曲和检验功效的增加。左偏程度受测量误差方差及其一阶协方差的相对大小控制,而与测量误差的均值大小和概率分布无关。测量误差方差增大,左偏更严重;正的一阶协方差可以减少和抵消统计量分布的向左偏离,而负的一阶协方差将加剧左偏的程度;一阶协方差接近于方差时,左偏程度很小。测量误差的方差相对较小时,其对单位根检验的影响可以忽略。This paper studies the limiting distribution of two statistics, T（ρ - 1） and T, of unit root test of time series with additive stationary measurement error, under two kinds of regression situations, with or without intercept. Theoretical analysis and Monte Carlo tests both show that the result of unit root test is susceptible to measurement error that makes the statistics left biased, resulting in overestimated size but improved power. The degree of left bias is decided by the relative size of variance and first order covariance, otherwise it has no relation with the mean and probability distribution of measurement error. Left bias becomes more serious when variance of measurement error increases, but lessens and is counteracted by positive first order covariance. However negative first order covariance may intensify left bias. Left bias is small when first order covariance is close to its variance. When variance of measurement error is relatively small, its influence to unit root test can be ignored.

关 键 词：测量误差 极限分布 单位根检验 

分 类 号：O212[理学—概率论与数理统计]